The shared image was DOCTORED. FACT: one of the ORIGINAL versions of the image was previously published in 2011, therefore it’s UNRELATED to the recent (2023) Turkey’s earthquake.
More in the EXPLANATION and REFERENCES section.
CATEGORY: Manipulated content.
SOURCE: Facebook, https://archive.ph/IOdwB (backup archive).
NARRATIVE: “This pic is some of those best rare pics I’ve ever seen. This is Imam e Jamia mosque in Turkey kissing hand of the dog which rescued and saved lives of 3 people tangled in debris. Last line is the theme “only being a man doesn’t matter, what matters is sincere service, no matter by whom”.”
Based on 7 Types of Mis- and Disinformation by First Draft News, classified as “Manipulated content: When genuine information or imagery is manipulated to deceive”. 
The SOURCE shared MANIPULATED content which caused a MISLEADING conclusion. FACT: the shared image was DOCTORED. One of the ORIGINAL versions of the image was previously published in 2011, therefore it’s UNRELATED to the recent (2023) Turkey’s earthquake.
One of the ORIGINAL versions of the image which was previously published in 2011, Grupa ZPR Media in 2011/10/27: “The mission of an animal pastor – as Tomasz Jaeschke says about himself – is one: to bless animals. Once, for six years, he celebrated masses for people, but after taking off his cassock, he did not depart from God.” (Google Translate) 
Other Related References
Fact-check article by Fars News in 2016: “According to Fars, the above claim about “kissing the hand of a dog that saved the lives of 3 people from the rubble of an earthquake by the imam of a city in Turkey” is not true. In addition, the above image is obtained by merging different images” (Google Translate) 
Google – News search result, keyword: “2023 turkey earthquake”.